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Prog. Theor. Phys. Supplement No.86 (1986) pp. 366-376
Supersymmetric Quantum Mechanics and Inverse Scattering
Waikwok Kwong and
Jonathan L. Rosner
Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637
(Received November 18, 1985)
Abstract:
The connection between supersymmetric quantum mechanics and the inverse scattering problem is utilized to construct symmetric reflectionless potentials with an arbitrary number of bound state levels. A relation between Backlund transformations and supersymmetry is explored. The transformations of interest relate a potential with a given spectrum to one with an additional bound state below all the rest. This potential may be regarded as an instantaneous solution of the Korteweg-de Vries (KdV) equation. The Backlund transformation is just that which adds a soliton to a multi-soliton KdV solution.
URL :
http://ptp.ipap.jp/link?PTPS/86/366/
DOI : 10.1143/PTPS.86.366
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